Parallelogram Side Length: Finding AC When Perimeter = 21 and AB = 7

Shown below is a parallelogram.

AB = 7

AC = 0.5X

The perimeter of the parallelogram is 21.

Calculate side AC.

Video Solution

Solution Steps

00:00 Find AC

00:03 Opposite sides are equal in parallelograms

00:10 They are also a pair of opposite sides therefore equal

00:21 The perimeter of the parallelogram equals the sum of its sides

00:35 Let's substitute appropriate values and solve for X

00:51 Let's isolate X

00:58 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Now, let's work through each step:

Step 1: The formula for the perimeter of a parallelogram is given by

P = 2(a + b)

where $a$ and $b$ are the lengths of the two pairs of sides.

Step 2: Substitute the known values into the formula. Here, let $a = AB = 7$ and $b = AC = 0.5X$ .

Perimeter $= 21$ , so:

21 = 2(7 + 0.5X)

Step 3: Solve for the unknown variable $X$ .

First, divide both sides of the equation by 2 to isolate the terms inside the parenthesis:

10.5 = 7 + 0.5X

Subtract 7 from both sides:

3.5 = 0.5X

Multiply both sides by 2 to isolate $X$ :

X = 7

Step 4: Determine the length of AC:

Substitute back to find $0.5X = AC$ :

AC = 0.5 \times 7 = 3.5

Therefore, the length of side AC is $3.5$ .